These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 23. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/23, 1/23, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 11/1, 12/1 13/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.138725) (-0.138160,-0.093930) (-0.092666,-0.089218) (-0.086228,-0.085207) (-0.081541,-0.080627) (-0.078177,-0.075709) (-0.073545,-0.072800) (-0.070107,-0.069431) (-0.067606,-0.065753) (-0.064114,-0.063548) (-0.061486,-0.060965) (-0.059554,-0.058111) (-0.053216,-0.052060) (-0.048097,-0.047151) (-0.043876,-0.043088) (-0.040336,-0.039669) (-0.037325,-0.036753) (-0.034732,-0.034237) (-0.032477,-0.032043) (-0.030496,-0.030113) (-0.028743,-0.028402) (-0.027180,-0.026876) (-0.025779,-0.025505) (-0.024515,-0.024267) (-0.023369,-0.023144) (-0.022326,-0.022120) (-0.021371,-0.021183) (-0.020495,-0.020322) ( 0.020322,0.020495 ) ( 0.021183,0.021371 ) ( 0.022120,0.022326 ) ( 0.023144,0.023369 ) ( 0.024267,0.024515 ) ( 0.025505,0.025779 ) ( 0.026876,0.027180 ) ( 0.028402,0.028743 ) ( 0.030113,0.030496 ) ( 0.032043,0.032477 ) ( 0.034237,0.034732 ) ( 0.036753,0.037325 ) ( 0.039669,0.040336 ) ( 0.043088,0.043876 ) ( 0.047151,0.048097 ) ( 0.052060,0.053216 ) ( 0.058111,0.059554 ) ( 0.060965,0.061486 ) ( 0.063548,0.064114 ) ( 0.065753,0.067606 ) ( 0.069431,0.070107 ) ( 0.072800,0.073545 ) ( 0.075709,0.078177 ) ( 0.080627,0.081541 ) ( 0.085207,0.086228 ) ( 0.089218,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-0.138907,-0.138019) -9/65 HST (-0.098076,-0.088511) -3/32 EXTENDED HST -> HST (-0.090886,-0.085964) -10/113 HST (-0.088259,-0.088212) -3/34 EXTENDED HST (-0.086991,-0.086922) -2/23 EXTENDED HST (-0.091491,-0.077953) -4/47 EXTENDED HST -> HST (-0.083396,-0.083270) -1/12 EXTENDED HST (-0.079575,-0.070944) -4/53 HST (-0.075017,-0.074983) -3/40 EXTENDED HST (-0.074099,-0.074049) -2/27 EXTENDED HST (-0.075630,-0.065123) -4/57 HST (-0.067307,-0.062854) -14/215 HST (-0.065111,-0.064760) -5/77 HST (-0.064535,-0.064497) -2/31 EXTENDED HST (-0.064621,-0.060972) -12/191 HST (-0.062535,-0.062465) -1/16 EXTENDED HST (-0.060980,-0.060759) -7/115 HST (-0.062364,-0.059090) -13/214 HST (-0.060623,-0.060589) -2/33 EXTENDED HST (-0.061192,-0.054499) -4/69 HST (-0.057702,-0.057682) -3/52 EXTENDED HST (-0.057158,-0.057128) -2/35 EXTENDED HST (-0.055584,-0.055528) -1/18 EXTENDED HST (-0.054753,-0.054339) -8/147 HST (-0.054351,-0.054176) -5/92 HST (-0.055615,-0.052686) -13/240 HST (-0.054067,-0.054041) -2/37 EXTENDED HST (-0.054856,-0.048838) -4/77 HST (-0.051732,-0.051716) -3/58 EXTENDED HST (-0.051294,-0.051270) -2/39 EXTENDED HST (-0.050023,-0.049977) -1/20 EXTENDED HST (-0.054145,-0.043459) -21/430 HST (-0.048791,-0.048770) -2/41 EXTENDED HST (-0.045445,-0.040438) -4/93 HST (-0.042863,-0.042852) -3/70 EXTENDED HST (-0.042561,-0.042545) -2/47 EXTENDED HST (-0.041682,-0.041651) -1/24 EXTENDED HST (-0.040454,-0.040409) -15/371 HST (-0.040575,-0.040242) -91/2252 HST (-0.040408,-0.040400) -4/99 EXTENDED HST (-0.041855,-0.037236) -4/101 HST (-0.039478,-0.039469) -3/76 EXTENDED HST (-0.039223,-0.039209) -2/51 EXTENDED HST (-0.038475,-0.038448) -1/26 EXTENDED HST (-0.038790,-0.034503) -4/109 HST (-0.036589,-0.036581) -3/82 EXTENDED HST (-0.036370,-0.036358) -2/55 EXTENDED HST (-0.035726,-0.035703) -1/28 EXTENDED HST (-0.036144,-0.032145) -4/117 HST (-0.034094,-0.034087) -3/88 EXTENDED HST (-0.033904,-0.033893) -2/59 EXTENDED HST (-0.033343,-0.033323) -1/30 EXTENDED HST (-0.033835,-0.030088) -4/125 HST (-0.031918,-0.031912) -3/94 EXTENDED HST (-0.031751,-0.031741) -2/63 EXTENDED HST (-0.031259,-0.031241) -1/32 EXTENDED HST (-0.031804,-0.028278) -4/133 HST (-0.030003,-0.029997) -3/100 EXTENDED HST (-0.029855,-0.029847) -2/67 EXTENDED HST (-0.029420,-0.029404) -1/34 EXTENDED HST (-0.028282,-0.028215) -5/177 HST (-0.028232,-0.028195) -9/319 HST (-0.028874,-0.027510) -17/603 HST (-0.028173,-0.028165) -2/71 EXTENDED HST (-0.027785,-0.027771) -1/36 EXTENDED HST (-0.027576,-0.027470) -8/291 HST (-0.027473,-0.027429) -5/182 HST (-0.028174,-0.026670) -13/474 HST (-0.027401,-0.027394) -2/73 EXTENDED HST (-0.026775,-0.026566) -105/3937 HST (-0.026670,-0.026663) -2/75 EXTENDED HST (-0.026598,-0.026500) -3/113 HST (-0.028630,-0.024275) -4/151 HST (-0.026322,-0.026310) -1/38 EXTENDED HST (-0.025646,-0.022795) -4/165 HST (-0.024195,-0.024192) -3/124 EXTENDED HST (-0.024099,-0.024094) -2/83 EXTENDED HST (-0.023815,-0.023804) -1/42 EXTENDED HST (-0.022797,-0.022773) -8/351 HST (-0.023472,-0.022061) -12/527 HST (-0.022732,-0.022723) -1/44 EXTENDED HST (-0.022176,-0.021946) -79/3581 HST (-0.022060,-0.022057) -3/136 EXTENDED HST (-0.021980,-0.021976) -2/91 EXTENDED HST (-0.021958,-0.021929) -7/319 HST (-0.021931,-0.021865) -3/137 HST (-0.023634,-0.020031) -4/183 HST (-0.021743,-0.021735) -1/46 EXTENDED HST (-0.080056,0.095345 ) 0/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "a*b*c*d");